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2x2 system a\sqrt{a}+ b\sqrt{b} = 134 , a\sqrt{b}+ b\sqrt{a} = 126

Source: Dutch NMO 2011 p4

September 6, 2019
algebrasystem of equationsradical

Problem Statement

Determine all pairs of positive real numbers (a,b)(a, b) with a>ba > b that satisfy the following equations: aa+bb=134a\sqrt{a}+ b\sqrt{b} = 134 and ab+ba=126a\sqrt{b}+ b\sqrt{a} = 126.
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